A generalisation in 2+1 dimensions of the Korteweg-de Vries (KDV) equation is related to the Schrodinger operator in the plane. Spectral data which only depend on one complex spectral parameter are introduced and the inverse problem is formulated as a delta problem. In opposition to what happens in the usual scattering scheme, the final formula for reconstructing the potential does not depend fictitiously on any extra parameter. The time evolution of the spectral data corresponding to a potential that evolves according to the KDV-like equation mentioned above is also obtained.
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Boiti et al. (1987) studied this question.
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